To simplify the expression $(x^2 - 4x + 4)(x^2 - 4x) + 3$, we will expand the product and then combine like terms. Step 1: Let $y = x^2 - 4x$. Substitute $y$ into the expression. The expression becomes $(y + 4)y + 3$. Step 2: Expand the expression in terms of $y$. $$ (y + 4)y + 3 = y^2 + 4y + 3 $$ Step 3: Substitute $y = x^2 - 4x$ back into the expanded expression. $$ (x^2 - 4x)^2 + 4(x^2 - 4x) + 3 $$ Step 4: Expand $(x^2 - 4x)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a = x^2$ and $b = 4x$. $$ (x^2 - 4x)^2 = (x^2)^2 - 2(x^2)(4x) + (4x)^2 = x^4 - 8x^3 + 16x^2 $$ Step 5: Expand $4(x^2 - 4x)$. $$ 4(x^2 - 4x) = 4x^2 - 16x $$ Step 6: Combine all the expanded terms. $$ (x^4 - 8x^3 + 16x^2) + (4x^2 - 16x) + 3 $$ Step 7: Combine like terms. $$ x^4 - 8x^3 + (16x^2 + 4x^2) - 16x + 3 $$ $$ x^4 - 8x^3 + 20x^2 - 16x + 3 $$ The simplified expression is: $$ \boxed{x^4 - 8x^3 + 20x^2 - 16x + 3} $$ Send me the next one 📸